Solve (vs)^3(2s)^-2(4r)^4

$$( v s ) ^ { 3 } ( 2 s ) ^ { - 2 } ( 4 r ) ^ { 4 }$$

Evaluate

$$64sv^{3}r^{4}$$

Solution Steps

Expand \left(vs\right)^{3}.

$$v^{3}s^{3}\times \left(2s\right)^{-2}\times \left(4r\right)^{4}$$

Expand \left(2s\right)^{-2}.

$$v^{3}s^{3}\times 2^{-2}s^{-2}\times \left(4r\right)^{4}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$v^{3}s^{3}\times \frac{1}{4}s^{-2}\times \left(4r\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$v^{3}s^{1}\times \frac{1}{4}\times \left(4r\right)^{4}$$

Expand \left(4r\right)^{4}.

$$v^{3}s^{1}\times \frac{1}{4}\times 4^{4}r^{4}$$

Calculate 4 to the power of 4 and get 256.

$$v^{3}s^{1}\times \frac{1}{4}\times 256r^{4}$$

Multiply \frac{1}{4} and 256 to get 64.

$$v^{3}s^{1}\times 64r^{4}$$

Calculate s to the power of 1 and get s.

$$v^{3}s\times 64r^{4}$$

Expand

$$64sv^{3}r^{4}$$

Solution Steps

Expand \left(vs\right)^{3}.

$$v^{3}s^{3}\times \left(2s\right)^{-2}\times \left(4r\right)^{4}$$

Expand \left(2s\right)^{-2}.

$$v^{3}s^{3}\times 2^{-2}s^{-2}\times \left(4r\right)^{4}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$v^{3}s^{3}\times \frac{1}{4}s^{-2}\times \left(4r\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$v^{3}s^{1}\times \frac{1}{4}\times \left(4r\right)^{4}$$

Expand \left(4r\right)^{4}.

$$v^{3}s^{1}\times \frac{1}{4}\times 4^{4}r^{4}$$

Calculate 4 to the power of 4 and get 256.

$$v^{3}s^{1}\times \frac{1}{4}\times 256r^{4}$$

Multiply \frac{1}{4} and 256 to get 64.

$$v^{3}s^{1}\times 64r^{4}$$

Calculate s to the power of 1 and get s.

$$v^{3}s\times 64r^{4}$$